Displaying similar documents to “Centered-Lindelöfness versus star-Lindelöfness”

A generic theorem in the theory of cardinal invariants of topological spaces

Aleksander V. Arhangel'skii (1995)

Commentationes Mathematicae Universitatis Carolinae

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Relative versions of many important theorems on cardinal invariants of topological spaces are formulated and proved on the basis of a general technical result, which provides an algorithm for such proofs. New relative cardinal invariants are defined, and open problems are discussed.

Eberlein spaces of finite metrizability number

István Juhász, Zoltán Szentmiklóssy, Andrzej Szymański (2007)

Commentationes Mathematicae Universitatis Carolinae

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Yakovlev [, Comment. Math. Univ. Carolin. (1980), 263–283] showed that any Eberlein compactum is hereditarily σ -metacompact. We show that this property actually characterizes Eberlein compacta among compact spaces of finite metrizability number. Uniformly Eberlein compacta and Corson compacta of finite metrizability number can be characterized in an analogous way.

Relatively compact spaces and separation properties

Aleksander V. Arhangel'skii, Ivan V. Yashchenko (1996)

Commentationes Mathematicae Universitatis Carolinae

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We consider the property of relative compactness of subspaces of Hausdorff spaces. Several examples of relatively compact spaces are given. We prove that the property of being a relatively compact subspace of a Hausdorff spaces is strictly stronger than being a regular space and strictly weaker than being a Tychonoff space.